The resistance of a wire of iron is 10 ohms and temp. coefficient of resistivity...

Khalil Jones

Khalil Jones

Answered question

2023-03-14

The resistance of a wire of iron is 10 ohms and temp. coefficient of resistivity is 5 \times 10^{−3}/^{\circ} C. At 20^{\circ} C it carries 30 milliamperes of current. Keeping constant potential difference between its ends, the temperature of the wire is raised to 120^{\circ} C. The current in milliamperes that flows in the wire is

Answer & Explanation

Veronella6nk

Veronella6nk

Beginner2023-03-15Added 6 answers

Step 1: Calculation of resistance at 120   C
Let variables at 20   C be marked by subscript 1 and at 120   C be marked by subscript 2.
Given that,
R 1 R 2 = 1 + α t 1 1 + α t 2
Where t 1 = 20 C and R 1 is resistance at t 1 and t 2 = 120 C and R 2 is resistance at t 2 .
We have,
R 1 = 10 Ω , α = 5 × 10 3 / C 10 R 2 = 1 + ( 5 × 10 3 × 20 ) 1 + ( 5 × 10 3 × 120 ) R 2 15 Ω
Step 2: Calculation of current at 120 C
when the potential difference is constant,
i 1 R i 1 i 2 = R 2 R 1 = 15 10 = 1.5
It is also provided,
i 1 = 30 m A i 2 = 301.5 i 2 = 20 m A
Therefore, current flowing through the circuit at 120 C is 20mA.


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